That sounds a lot like really wanting a soulmate and an open relationship.

That's a nice thing to have; I am not judging anyone. Just thinking how that would influence the dating website algorithm, marketing, and the utility this whole project would create.

If some people say they want X but they actually want Y... however other people say they want X and they mean it... and the algorithm matches them together because the other characteristics match, at the end they may be still unsatisfied (if one of these groups is a small minority, they will be disappointed repeatedly). This could possibly be fixed by an algorithm smart enough that it could somehow detect which option it is, and only match people who want the same thing (whichever of X or Y it is).

If there are many people who say they want X but really want Y, how will you advertise the website? Probably by playing along and describing your website mostly as a site for X, but providing obvious hints that Y is also possible and frequent there. Alternatively, by describing your website as a site for X, but writing "independent" blog articles and comments describing how well it actually works for Y. (What is the chance that this actually is what dating sites are already doing, and the only complaining people are the nerds who don't understand the real rules?)

Maybe there is a market in explicitly supporting open relationships. (Especially if you start in the Bay Area.) By removing some hypocrisy, the matching could be made more efficient -- you could ask questions which you otherwise couldn't, e.g. "how many % of your time would you prefer to spend with this partner?".